N/A — Exam

Question 27 • Precalculus

Which graph represents the polar curve r is equal to 1 plus sine of theta ?

Answer

Image with description On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, 2). It has a cardioid at (0, 0).

Image with description On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, negative 2). It has a cardioid at (0, 0).

Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (2, 0). It has a cardioid at (0, 0).

Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (negative 2, 0). It has a cardioid at (0, 0).

Explanation

For r = 1 + sin θ, when θ = π/2, r = 2, giving the point (0, 2). When θ = 3π/2, r = 0, so the curve has its cusp at the origin. The cardioid therefore opens upward and meets the y-axis at (0, 0) and (0, 2), matching choice A.

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